No, not necessarily. For an obvious example, if you use a 32-bit compiler on a 64-bit OS, you will usually have 32-bit ints.
The requirements in the C standard are pretty minimal. In addition to the minimum size requirements, there (ยง6.2.5 / 5):
An objectA '' plain intis the natural size suggested by the runtime architecture (large enough to contain any value in the range from INT_MINto INT_MAX, as defined in the header <limits.h>).
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